In this paper, the dynamic model is established for the two-link rigid-flexible manipulator, which is represented by nonlinear ordinary differential equations–partial differential equations (ODEs–PDEs). Based on the nonlinear ODE–PDE model, the boundary control strategy is designed to drive the manipulator to follow a given trajectory and eliminate the vibration simultaneously. Considering actuators saturation, smooth hyperbolic tangent function is introduced for dealing with control input constraints problem. It has been rigorously proved that the nonlinear closed-loop system is asymptotically stable by using LaSalle's invariance principle. Simulation results show that the proposed controller is effective.

References

References
1.
Han
,
Z.-J.
, and
Xu
,
G.-Q.
,
2010
, “
Exponential Stabilisation of a Simple Tree-Shaped Network of Timoshenko Beams System
,”
Int. J. Control
,
83
(
7
), pp.
1485
1503
.
2.
He
,
W.
,
Sun
,
C.
, and
Ge
,
S. S.
,
2014
, “
Top Tension Control of a Flexible Marine Riser by Using Integral-Barrier Lyapunov Function
,”
IEEE/ASME Trans. Mechatronics
,
20
(
2
), pp.
497
505
.
3.
Zhao
,
Z.
,
Liu
,
Y.
,
He
,
W.
, and
Luo
,
F.
,
2016
, “
Adaptive Boundary Control of an Axially Moving Belt System With High Acceleration/Deceleration
,”
J. Franklin Inst.
,
10
(
11
), pp.
1299
1306
.
4.
Li
,
Z.
,
Yang
,
C.
,
Su
,
C.-Y.
,
Deng
,
S.
,
Sun
,
F.
, and
Zhang
,
W.
,
2015
, “
Decentralized Fuzzy Control of Multiple Cooperating Robotic Manipulators With Impedance Interaction
,”
IEEE Trans. Fuzzy Syst.
,
23
(
4
), pp.
1044
1056
.
5.
Liu
,
Y.
,
Zhao
,
Z.
, and
He
,
W.
,
2016
, “
Boundary Control of an Axially Moving Accelerated/Decelerated Belt System
,”
Int. J. Robust Nonlinear Control
,
26
(
17
), pp.
3849
3866
.
6.
Wongratanaphisan
,
T.
, and
Cole
,
M. O. T.
,
2009
, “
Robust Impedance Control of a Flexible Structure Mounted Manipulator Performing Contact Tasks
,”
IEEE Trans. Rob.
,
25
(
2
), pp.
445
451
.
7.
Monje
,
C. A.
,
Ramos
,
F.
,
Feliu
,
V.
, and
Vinagre
,
B. M.
,
2007
, “
Tip Position Control of a Lightweight Flexible Manipulator Using a Fractional Order Controller
,”
IET Control Theory Appl.
,
1
(
5
), pp.
1451
1460
.
8.
Xu
,
G. Q.
,
Liu
,
D. Y.
, and
Liu
,
Y. Q.
,
2008
, “
Abstract Second Order Hyperbolic System and Applications to Controlled Network of Strings
,”
Siam J. Control Optim.
,
47
(
4
), pp.
1762
1784
.
9.
He
,
W.
,
Zhang
,
S.
, and
Ge
,
S. S.
,
2014
, “
Robust Adaptive Control of a Thruster Assisted Position Mooring System
,”
Automatica
,
50
(
7
), pp.
1843
1851
.
10.
Zhao
,
Z. J.
,
Liu
,
Y.
,
Guo
,
F.
, and
Fu
,
Y.
,
2017
, “
Modelling and Control for a Class of Axially Moving Nonuniform System
,”
Int. J. Syst. Sci.
,
48
(
4
), pp.
849
861
.
11.
He
,
W.
, and
Ge
,
S. S.
,
2011
, “
Robust Adaptive Boundary Control of a Vibrating String Under Unknown Time-Varying Disturbance
,”
IEEE Trans. Control Syst. Technol.
,
20
(
1
), pp.
48
58
.
12.
He
,
W.
,
He
,
X.
, and
Ge
,
S. S.
,
2016
, “
Vibration Control of Flexible Marine Riser Systems With Input Saturation
,”
IEEE Trans. Mechatronics
,
21
(
1
), pp.
254
265
.
13.
Chen
,
M.
,
Ge
,
S. S.
, and
Ren
,
B.
,
2011
, “
Adaptive Tracking Control of Uncertain Mimo Nonlinear Systems With Input Constraints
,”
Automatica
,
47
(
3
), pp.
452
465
.
14.
Wen
,
C.
,
Zhou
,
J.
,
Liu
,
Z.
, and
Su
,
H.
,
2011
, “
Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance
,”
IEEE Trans. Autom. Control
,
56
(
7
), pp.
1672
1678
.
15.
Liu
,
Z.
,
Liu
,
J.
, and
He
,
W.
,
2017
, “
Modeling and Vibration Control of a Flexible Aerial Refueling Hose With Variable Lengths and Input Constraint
,”
Automatica
,
77
, pp.
302
310
.
16.
Yang
,
X.
, and
Ge
,
S. S.
,
2014
, “
Backstepping Control and Active Vibration Control for a Free-Flying Space Robot With Rigid-Flexible Links by Singular Perturbation Approach
,”
IEEE International Conference on Information and Automation
(
ICIA
), Hailar, China, July 28–30, pp. 164–169.
17.
Khorrami
,
F.
, and
Jain
,
S.
,
1993
, “
Nonlinear Control With End-Point Acceleration Feedback for a Two-Link Flexible Manipulator: Experimental Results
,”
J. Rob. Syst.
,
10
(
4
), pp.
505
530
.
18.
Zhang
,
L.
, and
Liu
,
J.
,
2012
, “
Observer-Based Partial Differential Equation Boundary Control for a Flexible Two-Link Manipulator in Task Space
,”
Control Theory Appl. IET
,
6
(
13
), pp.
2120
2133
.
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